Apparatus for coupling light between input and output waveguides

ABSTRACT

An apparatus for coupling light between input and output waveguides includes a substrate, an input waveguide disposed on the substrate and comprising a first optical axis, and an output waveguide disposed on the substrate and comprising a second optical axis vertically offset from the first optical axis. A superlens is disposed on the substrate between the input waveguide and the output waveguide. The superlens has a middle optical axis and comprises a vertically graded refractive index film having a refractive index distribution n(y), where y is a vertical direction substantially perpendicular to the middle optical axis.

RELATED APPLICATIONS

The present patent document is a continuation-in-part of U.S. patentapplication Ser. No. 12/187,928, filed Aug. 7, 2008, which is a divisionof U.S. patent application Ser. No. 10/652,269, filed Aug. 28, 2003, nowU.S. Pat. No. 7,426,328, which claims the benefit of the filing dateunder 35 U.S.C. §119(e) of U.S. Provisional Patent Application Ser. No.60/406,704, filed Aug. 28, 2002. The present patent document is also acontinuation-in-part of U.S. patent application Ser. No. 10/708,536,filed Mar. 10, 2004, which claims the benefit of the filing date under35 U.S.C. §119(e) of U.S. Provisional Patent Application Ser. No.60/454,806, filed Mar. 14, 2003. All of the foregoing applications arehereby incorporated by reference in their entirety.

TECHNICAL FIELD

The present disclosure is related generally to lens structures and moreparticularly to light coupling devices for photonics.

BACKGROUND

In the photonics chip industry, one of the basic processes is thetransformation of a light beam from a large size to a small size (orvice versa) between two optical waveguides of different mode sizes.However, the light coupling efficiency between the two opticalwaveguides involved in this basic process is generally low. There are afew commonly used approaches in the present state of the art to make alens structure that addresses the above needs.

One approach involves using the property of light refraction at anoptical interface. By making an optical medium such as a glass into acertain shape such as a ball or sphere, a lens can be made to focus alight beam. U.S. Pat. No. 6,026,206, entitled “Optical Coupler UsingAnamorphic Microlens,” is an example of one such approach.

Another approach to address the needs is to create a GRIN distributionof an optical medium. Due to the GRIN distribution, the light beam bendsas it travels inside the medium. This property is used in achievinglight focusing. A commonly used example is an axially symmetric GRIN rodlens, which is used for collimating a light beam emitted from a singlemode fiber. U.S. Pat. No. 6,267,915, entitled “Production Method forObjects with Radially-Varying Properties,” U.S. Pat. No. 6,128,926,entitled “Graded Index Lens for Fiber Optic Applications and Techniqueof Fabrication,” and U.S. Pat. No. 6,172,817, entitled “Graded IndexLens for Fiber Optic Applications and Technique of Fabrication,” are afew examples of this approach.

For coupling of light between a single mode fiber and a semiconductorwaveguide based device (such as a semiconductor laser), the mostcommonly used coupling optics is a lensed fiber. Such a lensed fiber ismade by shaping the end of the fiber into a hemispherical or cylindricallens using lapping and polishing and/or melting means. U.S. Pat. No.5,845,024, entitled “Optical Fiber with Lens and Method of Manufacturingthe Same,” and U.S. Pat. No. 6,317,550, entitled “Lensed Optical Fiber,”elaborate upon such optical fiber with lens.

However, there are a few problems associated with the above-mentionedlenses. For a symmetric lens element, such as a GRIN rod lens, or a balllens or a tapered conical lensed fiber, the focused mode profile from acircular optical fiber is circular. As a semiconductor waveguide almostalways has an elliptical mode profile, there is a large mode mismatch,which inherently results in low light coupling efficiency. Thus, thecoupling efficiency for coupling light between a single mode fiber and asemiconductor waveguide based device cannot be very high. In fact, thecoupling efficiency is only as high as about 80% for such lenses.

For reducing the problem of mode mismatch and subsequently increasinglight coupling efficiency, wedge fibers can be used. There are generallytwo kinds of wedge fibers: single wedge fiber and double wedge fibers.Single wedge fibers have an elliptical focused beam spot with the longhorizontal axis spot size basically equal to that of the circular singlemode fiber spot size. However, as the horizontal axis mode spot size ofa semiconductor waveguide (such as a laser diode) is typically onlyabout 3 to 4 μm, and the beam spot size of a single mode fiber is about6 to 10 μm, there remains a mismatch in the horizontal mode size. Adouble wedge fiber addresses the problem of mismatch in horizontal modesize. Using a double wedge fiber, the horizontal mode size can be madeto match that of a semiconductor waveguide. However, the vertical spotsize cannot be made to match with that of a semiconductor waveguide.

The above disadvantage of vertical spot size mismatch is present in alloptical-interface-refraction based lenses (including those describedabove). This is due to the fact that the minimum vertical spot size forthese lenses is about 1.5 μm (for the near infrared opticalcommunication spectrum region) while the typical vertical mode size of asemiconductor waveguide is about 1 μm. In addition, for these lenses,especially lensed fibers, there is a large variation in the radius ofcurvature of the lens because each lens is made individually one at atime through processes, such as arcing or laser melting, that cannotguarantee high precision consistency. Thus, all the above-mentionedlenses will have a relatively low coupling efficiency, and there is alow consistency in the coupling efficiency.

Thus, what is needed in the photonics chip packaging industry is asuperlens that can provide a focused beam spot size, and canindependently achieve horizontal and vertical phase and/or wave-frontmatching with those of a semiconductor waveguide. In addition, thevertically focused spot size is preferably the order of about 1 μm inorder to match with that of a typical semiconductor waveguide. Such asuperlens may allow a light coupling efficiency well above 80% to becomepractically achievable.

BRIEF SUMMARY

An improved apparatus for coupling light between input and outputwaveguides is described herein. The apparatus includes an inputwaveguide disposed on the substrate and comprising a first optical axis,and an output waveguide disposed on the substrate and comprising asecond optical axis vertically offset from the first optical axis. Asuperlens is disposed on the substrate between the input waveguide andthe output waveguide. The superlens has a middle optical axis andcomprises a vertically graded refractive index film having a refractiveindex distribution n(y), where y is a vertical direction substantiallyperpendicular to the middle optical axis.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates the concept of light reflection, refraction and totalinternal reflection at an optical interface;

FIG. 2 shows the manner in which light is guided in a step refractiveindex waveguide, such as an optical fiber, through successive totalinternal reflection;

FIG. 3( a) shows ray optics picture of focusing a parallel light beamusing a lens and FIG. 3( b) shows computer simulated wave picture offocusing a parallel light beam using a lens;

FIG. 4 shows ray optics picture of light beam propagation in a gradedrefractive index (“GRIN”) optical medium;

FIG. 5( a) shows side view of vertically graded refractive indexdistribution and computer simulation of vertical focusing, FIG. 5( b)shows top view of horizontally curved surface lens and computersimulation of horizontal focusing and FIG. 5( c) shows athree-dimensional view of the invented lens structure;

FIG. 6( a) shows a computer simulation of vertical focusing pure gradedrefractive index distribution to a focal length or a quarter of thepitch of the GRIN medium and FIG. 6( b) shows a computer simulation ofhorizontal focusing a convex cylindrical input surface or sidewall;

FIG. 7 shows computer simulation of vertical focusing (a) when the GRINmedium thickness is equal to 16 μm, which is just a quarter of the pitchof the GRIN distribution, (b) when the GRIN medium thickness is equal to14 μm; (c) when the GRIN medium thickness is equal to 12 μm, (d) whenthe GRIN medium thickness is equal to 10 μm, (e) when the GRIN mediumthickness is equal to 8 μm, (f) when the GRIN medium thickness is equalto 6 μm and (g) when the GRIN medium thickness is equal to 4 μm;

FIG. 8 shows horizontal cylindrical lens and their correspondinghorizontally focused beam spot sizes for varying dimensions: (a)thickness T=10 μm, first radius R1=8 μm, second radius R2=8 μm, (b)thickness T=10 μm, first radius R1=10 μm, second radius R2=10 μm, (c)thickness T=10 μm, first radius R1=12 μm, second radius R2=12 μm, (d)thickness T=10 μm, first radius R1=14 μm, second radius R2=14 μm, (e)thickness T=10 μm, first radius R1=16 μm, second radius R2=16 μm, (f)thickness T=10 μm, first radius R1=18 μm, second radius R2=18 μm and (g)thickness T=10 μm, first radius R1=20 μm, second radius R2=20 μm;

FIG. 9( a) shows computer simulation of vertical focusing when a strongfocusing GRIN medium (with n₀=2.2 and n_(b)=1.5) has a thickness of 6 μmand FIG. 9( b) shows computer simulation of horizontal focusing of abi-convex cylindrical lens with refractive index n=2.2, first radius ofcurvature R1=10, second radius of curvature R2=−9 and lens thickness T=6μm; FIG. 9( c) shows an arbitrary curved surfaces to realize arbitraryphase and intensity profile transformation in the horizontal directionfor the input beam. FIG. 9( d) shows an arbitrary refractive indexprofile in vertical direction.

FIG. 10 shows measured focus spot sizes along with the correspondingoptical device: (a) size of about 10 μm by 10 μm from a standard singlemode fiber, (b) size of about 4 μm by 10 μl from a wedge fiber, (c) sizeof about 4 μm by 3.5 μm from a conical lensed fiber, (d) size of about 1μm by 4 μm from our superlens and (e) size of about 1 μm by 3.5 μm froma semiconductor laser;

FIGS. 11( a)-11(b) are schematic diagrams representing the use of twomaterials to realize a parabolic effective refractive indexdistribution;

FIGS. 11( c)-11(d) are graphs of the effective index distribution as afunction of position for the structure in FIGS. 11( a)-11(b);

FIG. 12 is a graph of transmittance as a function of the normalizedthickness of a thin layer of one optical medium sandwiched in anotheroptical medium;

FIGS. 13( a)-13(b) are graphs of a computer simulation of lightpropagation through a parabolic refractive index distribution realizedwith multiple materials and with two materials, respectively;

FIGS. 14( a)-14(b) are graphs of simulated light coupling from a GRINlens into a mode matched waveguide for a parabolic refractive indexdistribution realized with two materials and with multiple materials,respectively;

FIG. 15 is a scanning electron microscope (SEM) image of a GRINstructure realized by depositing alternating thin layers of twomaterials of different layer thickness on a flat silicon substrate;

FIGS. 16( a)-16(b) are graphs showing the measured focused spot profileand input spot profile for a one dimensional GRIN lens realized usingSiO₂ and TiO₂;

FIGS. 17( a)-17(d) are schematic diagrams illustrating process steps forfabricating a GRIN device from curved layers of two materials.

FIGS. 18( a)-18(e) show various embodiments of the superlens with (a)light transformed from one focus point to another with launching at themiddle optical axis of the superlens; (b) light transformed from onefocus point to another with launching at a position vertically offsetfrom the middle optical axis of the superlens; (c) a superlens with ahalf-parabolic index profile that transforms light to a larger modesize; (d) surface emission from a superlens with an output surface at anoblique angle to the superlens middle optical axis; and (e) a superlensspaced apart from input and output waveguides;

FIGS. 19( a)-19(e) shows side and top views of an optical apparatusincluding a superlens coupling a semiconductor waveguide and an opticalfiber according to several embodiments;

FIGS. 19( f)-19(h) show input and/or output waveguides having (f)concave, (g) convex and (h) arbitrarily shaped curvilinear surfaces;

FIGS. 19( i)-19(m) show a superlens having planar, convex, concave, orarbitrarily shaped curvilinear input and/or output surfaces according toseveral embodiments;

FIG. 20 is a flowchart depicting the method of fabricating a superlens;

FIG. 21 shows a scanning electron microscope (SEM) image of the dryetched vertical input sidewall of a superlens;

FIG. 22 shows a scanning electron microscope (SEM) image of the dryetched curved sidewall surface; and

FIG. 23 illustrates the idea of simultaneous multi-channel lightcoupling using a superlens array-packaging platform.

DETAILED DESCRIPTION OF THE DRAWINGS AND THE PRESENTLY PREFERREDEMBODIMENTS

The present disclosure relates to superlens for coupling light betweeninput and output waveguides that allows a change in the verticallocation of focus and/or in the mode size of the propagating light. Thesuperlens is capable of providing a wide variety of functionalities byusing different refractive index profiles, launching positions, andphysical lens shapes. Structures described herein may enableelectromagnetic beam transformation or spot size conversion between alarge-mode-size and a small-mode-size. In particular, the presentdisclosure relates to optical structures having an effective gradedrefractive index (GRIN) distribution in the vertical directionperpendicular to the optical axis of light propagation.

The optical structures may further include a lens-shaped opticalinterface structure perpendicular to the direction of light propagation.An apparatus that can control the size and the phase of anelectromagnetic beam and independently focus it in the vertical and/orhorizontal directions is described.

To improve the understanding of the present disclosure, fundamentalconcepts related to the invention are herein described.

Fundamental Concepts:

An electromagnetic wave is characterized by a wavelength and a frequencywith which it oscillates. Further, the electromagnetic wave travels at aspeed that depends on the medium through which it is traveling. Thespeed of the electromagnetic wave decreases as it travels from vacuum toa medium. The ratio of the speed of electromagnetic wave in vacuum (c)and the speed in the medium (v) is a property of the medium and isreferred to as the refractive index (n) of the medium.

When the electromagnetic wave travels through a medium, the frequency ofthe electromagnetic wave is unchanged while the wavelength is reducedfrom λ_(o) in vacuum to t_(eff)=λ_(o)/n in the dielectric medium.

Electromagnetic wave can be assumed to be a ray traveling in a straightline within a medium of the same refractive index if the size of themedium (such as a lens) is much greater than (about ten times) thewavelength of the electromagnetic wave. The electromagnetic waveundergoes refraction as well as reflection when it travels from onemedium to the other medium. For example, FIG. 1 shows an opticalinterface 110 between two media 120 and 130. Medium 120 has refractiveindex n; and medium 130 has refractive index n_(t). An electromagneticwave ray is reflected back into the first medium 120 and alsorefracted/transmitted into the second medium 130. According to the lawof reflection, the angle of incidence (θ_(i)) of the incidentelectromagnetic wave ray equals the angle of reflection (θ_(r)) of thereflected electromagnetic wave ray. Further, Snell's law of refractionstates that the refraction angle (θ_(t)) is related to the incidenceangle (θ_(i)) through the equationn_(i) sin θ_(i)=n_(t) sin θ_(t)

However, if n_(i)>n_(t), as θ_(i) increases to a particular value calledthe critical angle, θ_(t) will reach 90°, and afterwards, the incidentelectromagnetic ray is totally reflected as is shown for electromagneticray 140. This phenomenon is referred to as total internal reflection.The concept of total internal reflection is used in various practicalapplications. For example, total internal reflection is used to guideelectromagnetic wave through a step refractive index optical waveguideor fiber as shown in FIG. 2. In FIG. 2, incident electromagnetic wave202 strikes the wall of optical waveguide 204 at an angle that isgreater than the critical angle for the optical waveguide. Hence, theelectromagnetic wave undergoes total internal reflection resulting inthe transmission of the electromagnetic wave through the waveguide.

An optical interface between two media can be shaped into a curvedsurface. The curved surface so generated is also referred to as lens.For example, FIG. 3( a) shows a lens 310 that is constructed by shapingan optical interface into a convex or concave curved surface form. Aparallel beam of electromagnetic wave can be regarded as being made upof a number of parallel rays 320. As shown in FIG. 3( a), curved surfacelens 310 can be made to enable parallel incident rays 320 to focus to asingle point 330 in space. This is because the outer rays are refractedmore than the central rays as governed by Snell's law of refraction sothat all the rays converge to one point.

However, Snell's law is based on the assumption that the electromagneticwave has infinite wavelength. In reality, an electromagnetic wave has afinite wavelength; hence the focused electromagnetic wave beam cannothave an infinitely small spot size but a finite spot size. For example,FIG. 3( b) shows a computer simulation of a focusing lens based on thewave theory and it can be seen that the focused electromagnetic wavebeam has a limited spot size 340 with a certain intensity distribution.

The refractive index of a medium can be constant or varying from onepoint in the medium to the other. For example, FIG. 4 shows a gradedrefractive index (“GRIN”) optical medium 400. The material of GRINoptical medium 400 has refractive index n(r) that decreases continuouslyfrom a value of n₀ at the central or middle axis (r=0) to a value ofn_(b) at the outside border (r=a). The distance r=a is defined as thedistance from the central axis to the border of the GRIN medium. In thisexample, n(r) has a parabolic refractive index distribution given by theformula:

${{n(r)} = {n_{o}\lbrack {1 - {\Delta( \frac{r}{a} )}^{2}} \rbrack}},{{{where}\mspace{14mu}\Delta} = {\frac{n_{0} - n_{0}}{n_{0}}.}}$

This refractive index distribution causes electromagnetic wave rays 410propagating longitudinally through GRIN optical medium 400 to bendtowards the central axis and to be periodically refocused. If GRINoptical medium 400 is cut to the right length, the GRIN optical medium400 can function as a lens to focus or expand and collimate a beam ofelectromagnetic wave. The focal length (f) (also called a quarter of thepitch) of such a GRIN medium is approximated by the following formula.

$f = \frac{a\;\pi}{2\sqrt{2\Delta}}$

In general, the focused spot size for any light beam or pulse is finite.The shorter the focal length of the lens, the smaller the focused spotsize. Accordingly, a smaller focused spot size can be achieved byincreasing Δ (which is dominated by the index change between the centralaxis and the outside border), by decreasing α (the distance between thecentral axis and the outside border), or both. At the same time, thereis a physical diffraction limit; consequently, the smallest focused spotsize of any wave will only be about the size of the wavelength in themedium where focusing occurs. In the case of a GRIN lens, the focusedlight beam is located near the central axis, where the refractive indexis the highest. Hence, if a high refractive index material is used atthe central axis, a much smaller diffraction limited beam spot size canbe achieved because the wavelength of light in a material is equal tothe vacuum wavelength divided by the refractive index of the material.If the focused light beam is coupled into another mode matchedwaveguide, a highly efficient light coupling between the GRIN lens andthe waveguide can be achieved, as will be described further below.

For example, an apparatus may combine a vertically GRIN multi-layerstructure with a curved sidewall surface lens structure. Thiscombination creates a two-dimensional lens that can independently focusan electromagnetic wave beam in the vertical and horizontal directions.In a preferred embodiment, the electromagnetic wave beam is a lightbeam. The combined structure may be referred to as a superlens. FIGS. 5(a), 5(b) and 5(c) show a preferred embodiment of the superlens. FIG. 5(a) shows the side view of a vertically GRIN lens structure. FIG. 5( b)gives the top view of the preferred horizontally curved surfacecylindrical lens structure, and FIG. 5( c) shows a 3-dimensional view ofthe preferred lens structure.

The superlens may be used for simultaneous focusing of a light beam tothe same focal plane along the optical axis in both the verticaldirection and the horizontal direction. Independent control for focusingthe light beam also allows a user to offset the vertical and horizontalfocal planes. Further, the superlens allows the user to control thephase or wavefront of the incident light beam in such a way that thefocused light beam can be deliberately made properly astigmatic. Thismay be used to match desired offset for some channel optical waveguidedevices, such as some semiconductor lasers for which the vertical andhorizontal beam waists are not at the same location along the opticalaxis. The method to control vertical and horizontal focusing is furtherdescribed using FIG. 6( a) and FIG. 6( b).

FIG. 6( a) and FIG. 6( b) respectively show computer simulation ofvertical focusing a pure GRIN distribution and horizontal focusing aconvex cylindrical input surface or sidewall. For the sake ofillustration, it is assumed that superlens 600 has a height of 12 μm anda width of 12 μm. Further, the light beam is circular in shape and has adiameter of 10 μm. The diameter of the light beam corresponds to atypical mode size of a standard single mode optical fiber at awavelength of 1.55 μm in vacuum. Thickness of superlens 600 is assumedto be 16 μm, which is equal to the focal length of the vertical GRINmedium. This ensures that a parallel beam incident on superlens 600 isvertically focused with the vertical focal plane substantially close tothe output or exit optical interface. Note that the example is chosenonly for the purpose of illustration, and in no way should it beconstrued as limiting the scope of the invention, which, in turn, isdetermined by the appended claims.

Horizontal focusing superlens 600 is done by creating a horizontalcurved sidewall on the input side of superlens 600. The curved surfacecan be of various forms such as cylindrical, spherical, aspherical andtoric. In a preferred embodiment, a convex cylindrical curved surface isused for the superlens. Further, the horizontal and vertical focusingare done in a common focal plane by proper selection of the radius ofcurvature R₁ of the cylindrical curved surface.

A feature of the horizontal and vertical focusing is that the depth offocus for the horizontal focusing is larger than that for the verticalcase. This is because the vertical focusing power is higher than thehorizontal one or the vertically focused spot size is smaller than thehorizontal one.

The method of vertical and horizontal focusing is now further described.For the sake of illustration, assume that superlens 600 has a GRINdistribution n(r)=n₀[1−Δ(r/a)²], where Δ=(n₀−n_(b))/n₀, δn=n₀−n_(b) andvertical focal length (f) is f=aπ/(2√2 Δ). Possible methods toindependently control the spot size vertically as well as horizontallyare described herein after.

One simple method to adjust the vertical focused spot size to a largevalue is to etch superlens 600 to a smaller total thickness (also calledlength) so that electromagnetic beam focusing occurs in the next uniformoptical medium. In most practical cases, the next uniform optical mediumis air with a refractive index of one. This method is further describedusing FIG. 7( a) to FIG. 7( g).

FIG. 7( a) to FIG. 7( g) show the computer simulation of an exemplaryvertical GRIN medium with refractive index distributionn(y)=2.05-0.3(y/6 μm)² with various total thickness and the computersimulation of light beam focusing for each case. This distribution ischosen only for the purpose of illustration, and there are numerousother distributions that achieve the same result. The parallel circularinput light beam size is assumed to be 10 μm, which corresponds to thetypical mode size of a standard single mode optical fiber. FIG. 7( a) toFIG. 7( g) show that with the reduction of the total length or thicknessof the vertically GRIN medium from 16 μm to 4 μm, the vertically focusedlight beam spot size is monotonically increased. Additionally, the focalplane is also moved towards the input side of the GRIN medium.

There is a practical limit to the smallest total thickness of the lens,and as photolithography is used to make a dry etch mask, a reasonablethickness limit is about 4 μm. Since the vertically focused spot sizeincreases as the lens thickness decreases, and also there is a limit tothe practical lens thickness, one method to enhance the range ofvertically focused spot size is to come up with a few standard verticalGRIN distributions. Some of the distributions have very strong focusingpower and others have less focusing power. Further, each GRINdistribution may be etched into different lens thickness. For example,to cover a range of vertical spot size from 1 μm to 5 μm, two standardGRIN distributions are such that one has a smallest focused spot size of1 μm and the other has a smallest focused spot size of 3 μm.Additionally, in FIG. 7( a) to FIG. 7( g), along with the decrease inthe GRIN medium thickness, the focused spot size can actually becontrolled to vary from around 1 μm to around 3 μm.

While vertical focusing may be controlled by controlling the thicknessof the superlens, horizontal focusing may be controlled by giving propershape to the curved sidewall. This control involves design and etchingof the curved input and output sidewalls to adjust the sidewall surfaceprofile. In one preferred embodiment, the design should be such that thehorizontal focal plane coincides with the vertical focal plane and thehorizontal focused spot size can be controlled to a desirable value. Themethod to control horizontal spot size is further explained using FIG.8( a) to FIG. 8( g).

FIG. 8( a) to FIG. 8( g) corresponds to the case of FIG. 7( d) in whichthe vertical GRIN medium has a thickness of 10 μm and the vertical focalplane is located at about 12 μm from the input side. Horizontal focusingis a function of the radius of curvature of the input and outputcylindrical sidewalls. In this example, the first radius R1 of the inputcylindrically convex surface is designed to be equal to second radius R2of the output cylindrically concave surface. By keeping the two radii ofcurvature of the two sidewalls substantially equal to each other butwith the first one convex and the second one concave, the focal plane ismore or less maintained at the same location of about 12 μm from theinput side of the superlens. FIG. 8( a) to FIG. 8( g) show that as theradius of curvature of the horizontally cylindrical sidewall isincreased, the focused electromagnetic beam size also increases.

A point to note is that in the computer simulation the refractive indexof the superlens medium is assumed to be equal to 2.05, which is thecentral refractive index of the assumed GRIN distribution. Centralrefractive index is chosen over the average refractive index for theGRIN distribution because most of the optical energy of a Gaussianelectromagnetic beam (this is the case for an electromagnetic beam in anoptical fiber or in a semiconductor channel waveguide) is located in thecentral region. Furthermore, in this case the optical axis of the inputand output waveguides are aligned along the central axis of thesuperlens. In addition, since the GRIN distribution is assumedparabolic, a major part of the GRIN distribution has a refractive indexthat is close to the central refractive index.

Further, the vertically central portion of the beam is horizontallyfocused more strongly than the vertical non-border portion of the beam.This is due to the difference of the refractive index in the verticaldirection as one moves from the central axis to the border. This slightdeviation causes the focused electromagnetic beam not to be perfectlyGaussian in the horizontal direction. However, the computer simulationshows that the influence to the overall light coupling efficiency isminimal once the mode size and phase are matched for the central portionof the light beam. In an alternative embodiment, this problem can beovercome by etching the input and the output sidewalls of the lens intoa three dimensional curved surface such that along with the departurefrom the vertical central region of the GRIN distribution, thehorizontal radius of curvature is made to have a smaller value graduallyto balance out the effect of the refractive index decrease. This ensuresthat the vertical border portion of the electromagnetic beam is focusedby the same amount as the vertical central portion of the beam.

The input sidewall may be taken to be convex and output sidewall to beconcave. However, the above method for horizontal and vertical focusingcan also be applied for other shapes of sidewalls. Furthermore, if thethickness of the superlens is very small, the lens may achieve arelatively small horizontal focused spot size and at the same time keepthe horizontal focal plane to coincide with the vertical focal plane.This feature is further highlighted using the example described in FIG.9( a) and FIG. 9( b).

The example in FIG. 9( a) and FIG. 9( b) shows an alternate embodimentof a superlens 900 that has convex input and output sidewalls. In FIG.9( a), the vertical parabolic GRIN medium has a relatively strongfocusing power with refractive index at the center n₀=2.2 and refractiveindex at the border n_(b)=1.5 and the thickness of the lens T=6 μm. Thevertical focal plane is located in air at about 8.5 μm from the inputside of the superlens. FIG. 9( b) shows the horizontal structure ofsuperlens 900 and the computer simulation of light propagation. Theassumed values for the horizontal superlens curved surface are:refractive index n=2.2, first radius of curvature R1=10, second radiusof curvature R2=−9 and superlens thickness T=6 μm. The computersimulation in FIG. 9( a) and (b) shows that the 10 μl wide parallelincident light beam can be made to focus horizontally at the samedistance from the input surface as that for the vertically focused beam.This example shows that in addition to the vertically GRIN distribution,both the first or input sidewall and the second or output sidewall canbe made to have different sidewall surface profiles to accommodatevarious requirements and applications.

The method of horizontal and vertical focusing described above allowstransformation of an electromagnetic beam to various circular orelliptical or other desirable intensity profiles. Furthermore, themethod also accommodates various phase matching needs. For example, inthe case of beam size transformation from a single mode fiber to asemiconductor channel waveguide, the vertically focused beam size can becontrolled to vary from 0.5 μm to 10 μm, and the horizontally focusedbeam size can be controlled to vary from 2 μm to 10 μm. Such a widerange is beneficial to the current photonics chip packaging industrysimply because other lenses known in the art cannot focus a light beamto less than 1.5 μm in the vertical direction, and the requiredvertically focused beam size is about 1 μm, which can be easily achievedwith superlens described herein. As the horizontal curved surfaces aredefined by lithography and etching, arbitrary curved surfaces can beformed to realize arbitrary phase and intensity profile transformationin the horizontal direction for the input beam. An example of sucharbitrary profile is illustrated in FIG. 9( c), wherein the front andback curve surfaces of the lens have curvilinear shape shown in 1000.Likewise, as the graded refractive index profile can be fabricated bymaterial deposition, an arbitrary refractive index profile can be formedto realize arbitrary phase and intensity profile transformation in thevertical direction for the input beam. An example of such arbitraryprofile is illustrated in FIG. 9( d), wherein the refractive index ispeaked at a location below the middle of the lens with the varyingrefractive index profile n(y) shown in 1100.

The advantage of the improved technology over the existing technology isfurther highlighted using FIG. 10. FIG. 10 gives a comparison of themeasured light output spot size from a single mode fiber as shown inFIG. 10( a), a wedge fiber as shown in FIG. 10( b), a conical lensedfiber as shown in FIG. 10( c), an exemplary superlens as shown in FIG.10( d) and a standard semiconductor laser as shown in FIG. 10( e). Thefocused spot size from the superlens shown in FIG. 10( d) matches verywell with the spot size of the measured semiconductor laser, while thereis a relatively large mismatch for either the wedge fiber or theconically tapered lensed fiber. Furthermore, the superlens also achievesa coupling efficiency that is about 10 to 20% higher than the existingcommercially available conical lensed fibers or wedge fibers.

The optical medium on the left of the superlens is assumed to be thesame as the optical medium on the right of the superlens. However, theoptical medium on the left of the superlens can also be different fromthe optical medium on the right of the superlens. This optical mediummay be an optical fiber. Further, there can be a small air gap betweenthe optical fiber end face and the superlens input sidewall.

An anti-reflection coating may be deposited on both the left and theright sidewall of the superlens to substantially reduce reflection atthe two optical interfaces. For example, on the left side, if there is asmall air gap between the optical fiber end face and the superlens inputsidewall, then an anti-reflection coating can be deposited on both thefiber-to-air interface and the air-to-superlens interface to increaselight transmission and therefore increase light coupling efficiency. Theanti-reflection coating design depends on the refractive indexdistribution of the superlens, and may be based on either the centralrefractive index or the average refractive index or an optimizedequivalent refractive index that will lead a maximum light transmission.

The light transmission efficiency can be further improved by filling theair gap with a third optical medium. Such a medium can be properlyselected to have a refractive index that matches the fiber corerefractive index. The matching of refractive index between the fibercore and third optical medium ensures that there is only one opticalinterface between the fiber core and the superlens material. Theanti-reflection coating can then be properly designed to maximize lighttransmission across this interface.

Similarly, on the right side of the lens, a semiconductor waveguide canbe butt-joined to the superlens with a tiny air gap. Again,anti-reflection coatings can be deposited on either the superlenssidewall, or the semiconductor end face (depending on whether this isneeded) or on both surfaces. In a similar way, the air gap can be filledwith another optical medium, which may or may not need to serve anyindex matching purposes. For example, a fiber can be placed on the leftside of the superlens and a photonic chip on the right side of thesuperlens. In this case both the left air gap and the right air gap arefilled with the same optical medium such as an optical gel or atransparent optical polymer that is refractive index matched to thefiber core. The anti-reflection coating can then be deposited on therequired surfaces to maximize light transmission.

The GRIN distribution is not limited to parabolic distribution butincludes half-parabolic and other asymmetric or arbitrary distributions.For example, a proper choice of the GRIN distribution (not necessarilyparabolic) can used to match a focused light intensity profile that isnot Gaussian. Further, the electromagnetic wave spectrum covers allwavelength regions such as visible, infrared, radio frequency (RF), andTeraHertz waves.

It will also be appreciated that GRIN devices may allow for fine controland tuning of the refractive index and refractive index distribution toachieve a precise, arbitrary refractive index profile, thereby allowingprecise shaping of the optical spot size and mode (wavefront) profile oftransmitted light. Thus, such multilayer devices are also suitable foruse in a variety of optical applications, including applications wherethe difference in refractive index is small (e.g., less than 0.2).

In principle, a graded refractive index distribution can be constructedfrom multiple thin layers of optical media with different refractiveindices. If the layer thickness is small enough, there is a negligibledifference in the focusing effect between a continuously gradedrefractive index distribution and a step graded refractive indexdistribution provided by multiple thin layers of materials withdifferent refractive indices. For example, a parabolic refractive indexdistribution can be produced by depositing multiple thin layers ofdifferent materials selected so that the refractive index decreases withdistance from the central axis.

Two (or more) materials having a relatively large refractive indexdifference may be employed to create a structure having a gradedrefractive index (e.g., a parabolic distribution). By using a highrefractive index material such as silicon (n=3.4), the refractive indexat the central axis of the parabolic GRIN structure can be made quitehigh, and hence the spot size of the focused light beam can be quitesmall (e.g., less than 0.5 μm for light having a wavelength of 1.5 μm inair).

When an optical medium with a dimension that is substantially smallerthan the effective wavelength of light is embedded in another opticalmedium of a different refractive index, the result is an effectiverefractive index with a value between those of the two optical media.FIGS. 11( a)-11(d) illustrate the principle. A medium 200 provides anapproximately continuous parabolic refractive index distribution byusing multiple layers 205 of materials having different refractiveindexes as shown in FIG. 11( a). Each layer 205 is constructed from anumber of thin layers 212, 214 of two materials of different refractiveindices, as shown in FIG. 11( b). Each material's optical thickness issubstantially less than the effective wavelength of light in thematerial. The effective refractive index 215, illustrated in FIGS. 11(c)-11(d), is approximately

${n_{eff} = \frac{{n_{1}L_{1}} + {n_{2}L_{2}}}{L_{1} + L_{2}}},$where n₁ and n₂ are the refractive indexes of the two materialsrespectively, and L₁ and L₂, are the total thickness of the respectivematerials within a local region larger than the effective wavelength ofthe light. This can be generalized to a medium with a mixture of twoparticles with different refractive indices, in which

${n_{eff} = \frac{n_{2}\lbrack {{\frac{V_{1}}{V_{2}}\frac{n_{1}}{n_{2}}} + 1} \rbrack}{\lbrack {\frac{V_{1}}{V_{2}} + 1} \rbrack}},$in which V₁ and V₂ are the volumes of the first and second materials.Other layers in medium 200 are made of the same materials, but withdifferent thicknesses L₁ and L₂, thereby providing different n_(eff).

There are concerns about the effectiveness of using two materials toachieve the effect of a real continuous refractive index distribution.One concern is the light transmission efficiency through the manyoptical interfaces of the structure. A second concern is how effectivelythis structure focuses light. A third concern is the total amount oflight that will be lost when light is focused using this structure.These concerns are now addressed.

High light transmission efficiency can be provided by using sufficientlythin layers of the two materials. As is generally known in the art andillustrated in FIG. 12, when a light beam shines through a thin film 310of thickness d, having a refractive index n₂, sandwiched in anotheroptical medium 312, the light transmittance (defined as the amount oflight energy transmitted through the film divided by the amount of lightenergy incident onto the film) is given by

${T(d)} = {\frac{I_{trans}}{I_{inc}} = \frac{( {1 - R} )^{2}}{( {1 - R} )^{2} + {4R\;{\sin^{2}( {k_{\bot}d} )}}}}$where

${k_{\bot} = {\frac{2\pi}{\lambda_{eff}} = {\frac{2\pi\; n_{2}}{\lambda}\cos\;\theta}}},$with λ being the wavelength of light in vacuum, θ being the angle ofrefraction in the thin film 310, and R being the reflectance of the thinfilm. FIG. 12 shows the transmittance of light as a function ofd/λ_(eff) for a light beam traveling from silica (SiO₂, n₁=1.45) througha very thin film (thickness d) of titania (TiO₂, n₁=2.35) into silicaagain. It can be seen that when d/λ_(eff) is less than 0.1, more than90% of the light will be transmitted. Hence, a general guideline is thatwhen the thickness of the thin film is less than about

$\frac{\lambda}{10n_{2}\cos\;\theta},$more than 90% of the light will pass through the film. If the light beamshines onto the film at normal incidence (i.e. θ=θ°), the single layerfilm thickness is advantageously chosen to be less than

$\frac{\lambda}{10n_{2}},$which is about 66 nm for TiO₂ and about 100 nm for SiO₂. In GRIN-lensfocusing applications, the light wave travels paraxially along thecentral axis, so that the angle θ varies from 90° to about 60°.Accordingly, the fraction of light transmitted is generally more than95% if single layer thicknesses less than

$\frac{\lambda}{10n_{2}}$are used.

To evaluate the focusing power of the GRIN device, light wavepropagation was simulated for a first GRIN lens having a parabolicrefractive index distribution made up of thin layers of numerousdifferent materials, substantially approximating a continuous indexdistribution, and for a second GRIN lens made up of layers of only twomaterials. FIGS. 13( a)-13(b) show the simulation result for a parabolicrefractive index distribution of

${{n(r)} = {n_{0}\lbrack {1 - {\Delta( \frac{r}{a} )}^{2}} \rbrack}},$with a=5 μm, n₀=1.75 and n_(b)=1.45. FIG. 13( a) shows results for asubstantially continuous GRIN lens, and FIG. 13( b) shows results for atwo-material GRIN lens. As can be seen, both GRIN lenses have similarfocal lengths and focused spot sizes.

To evaluate the energy loss for light propagating longitudinally throughthe device, the optical energy flow was calculated based on integrationover space of the standard electromagnetic energy flow vector {rightarrow over (S)}={right arrow over (E)}×{right arrow over (H)}, where{right arrow over (E)}×{right arrow over (H)} are the electric andmagnetic fields. FIGS. 14( a)-14(b) show simulation results for atwo-material GRIN lens and a many-material GRIN lens, respectively. Inboth simulations, it has been assumed that there is no materialabsorption of light and all the interfaces are perfect. Each GRIN lensextends from point A to point D, so that the focal point is just outsidethe GRIN lens. A semiconductor waveguide made of indium phosphide (InP),with its mode matched to the focused beam profile, extends from point Bto point C, leaving an air gap of 1 μm between the GRIN lens and thesemiconductor waveguide. Antireflection coatings have been included onboth the GRIN lens end face and on the InP waveguide end face. Table 1shows light energy transmission efficiency for each GRIN lens. Thetwo-material case is not significantly different from the substantiallycontinuous case.

TABLE 1 Two- material Substantially case Continuous case Fraction oflight energy passed 99.9% 98.8% through the GRIN lens from A to BFraction of light energy passed from B 99.7% 99.5% to C (including modematching) Fraction of light energy within the InP 95.6% 98.2% waveguideat C (i.e., within 3× width of the waveguide) Overall couplingefficiency 95.3% 97.7%

The foregoing analyses indicate that a GRIN device made up ofalternating layers of two or more different materials can provide hightransmission efficiency, a short focal length, a small focused spotsize, and acceptably low energy loss when coupling to a small mode sizewaveguide or other optical components.

The physical size of the GRIN device can also be varied. For example, atwo-material device could be constructed for coupling light between asemiconductor laser or detector and a standard multimode fiber, whichtypically has a mode size of about 50 to 65 microns. It can also be usedto couple light from a one dimensional or two dimensional semiconductorlaser array or laser bar into a single mode fiber, e.g., for opticallypumping an erbium doped fiber amplifier.

In one example, a large number (e.g., 306) of alternating thin layers ofsilica (SiO₂) and titania (TiO₂) may be deposited on a flat siliconsubstrate. The thickness of each layer (in nm) for this embodiment islisted in Table 2. A thicker buffer layer of SiO₂ (1 μm) is depositedfirst in order to separate the GRIN device from the substrate materialso that light will not leak into the substrate. Aside from the bufferlayer, the thicknesses of the silica layers range from 20 nm to 70 nm,and the thicknesses of the titania layers range from 20 nm to 80 nm. Inregions where the effective index of refraction is high, titanic layersare near their thickest while silica layers are near their thinnest; inregions where the effective index is low, the reverse applies.

FIG. 15 shows an scanning electron microscope (SEM) image of such astructure deposited on a flat Si substrate, and FIG. 16( a) shows themeasurement result of such a structure acting as a one dimensional GRINlens to focus a light beam from a standard single mode fiber into anelliptical beam; as a comparison the output beam profile from a standardsingle mode fiber is shown in FIG. 16( b).

It should be noted that a planar layered structure may focus light onlyin the direction transverse to the plane of the layers (the verticaldirection for horizontal layers on a substrate). In the lateral orhorizontal direction, light beam size transformation can be achievedusing tapered waveguide structures.

TABLE 2 Mtl nm TiO2 60 SiO2 20 TiO2 50 SiO2 20 TiO2 60 SiO2 20 TiO2 50SiO2 20 TiO2 60 SiO2 20 TiO2 50 SiO2 20 TiO2 60 SiO2 20 TiO2 50 SiO2 20TiO2 80 SiO2 30 TiO2 80 SiO2 30 TiO2 80 SiO2 30 TiO2 80 SiO2 30 TiO2 80SiO2 30 TiO2 80 SiO2 30 TiO2 80 SiO2 30 TiO2 80 SiO2 30 TiO2 50 SiO2 20TiO2 80 SiO2 30 TiO2 50 SiO2 20 TiO2 50 SiO2 20 TiO2 50 SiO2 20 TiO2 50SiO2 20 TiO2 50 SiO2 20 TiO2 50 SiO2 20 TiO2 50 SiO2 20 TiO2 50 SiO2 20TiO2 50 SiO2 20 TiO2 70 SiO2 30 TiO2 S0 SiO2 20 TiO2 70 SiO2 30 TiO2 70SiO2 30 TiO2 70 SiO2 30 TiO2 S0 SiO2 20 TiO2 40 SiO2 20 TiO2 S0 SiO2 20TiO2 40 SiO2 20 TiO2 70 SiO2 30 TiO2 40 SiO2 20 TiO2 70 SiO2 30 TiO2 40SiO2 20 TiO2 70 SiO2 30 TiO2 40 SiO2 20 TiO2 40 SiO2 20 TiO2 40 SiO2 20TiO2 40 SiO2 20 TiO2 40 SiO2 20 TiO2 40 SiO2 20 TiO2 40 SiO2 20 TiO2 40SiO2 20 TiO2 40 SiO2 20 TiO2 40 SiO2 20 TiO2 40 SiO2 20 TiO2 S0 SiO2 30TiO2 40 SiO2 20 TiO2 50 SiO2 30 TiO2 40 SiO2 20 TiO2 S0 SiO2 30 TiO2 40SiO2 20 TiO2 30 SiO2 20 TiO2 40 SiO2 20 TiO2 30 SiO2 20 TiO2 40 SiO2 20TiO2 40 SiO2 30 TiO2 40 SiO2 20 TiO2 40 SiO2 30 TiO2 40 SiO2 20 TiO2 40SiO2 30 TiO2 30 SiO2 20 TiO2 30 SiO2 20 TiO2 30 SiO2 20 TiO2 30 SiO2 20TiO2 30 SiO2 20 TiO2 30 SiO2 20 TiO2 30 SiO2 20 TiO2 30 SiO2 20 TiO2 30SiO2 20 TiO2 40 SiO2 30 TiO2 40 SiO2 30 TiO2 40 SiO2 30 TiO2 40 SiO2 30TiO2 40 SiO2 30 TiO2 40 SiO2 30 TiO2 40 SiO2 30 TiO2 20 SiO2 20 TiO2 40SiO2 30 TiO2 20 SiO2 20 TiO2 40 SiO2 30 TiO2 20 SiO2 20 TiO2 40 SiO2 30TiO2 20 SiO2 20 TiO2 20 SiO2 20 TiO2 40 SiO2 30 TiO2 20 SiO2 20 TiO2 20SiO2 20 TiO2 20 SiO2 20 TiO2 20 SiO2 20 TiO2 20 SiO2 20 TiO2 20 SiO2 20TiO2 20 SiO2 20 TiO2 20 SiO2 20 TiO2 20 SiO2 20 TiO2 20 SiO2 20 TiO2 20SiO2 20 TiO2 20 SiO2 20 TiO2 20 SiO2 20 TiO2 20 SiO2 20 TiO2 20 SiO2 20TiO2 20 SiO2 20 TiO2 20 SiO2 40 TiO2 30 SiO2 20 TiO2 20 SiO2 20 TiO2 20SiO2 40 TiO2 30 SiO2 20 TiO2 20 SiO2 20 TiO2 20 SiO2 40 TiO2 30 SiO2 20TiO2 30 SiO2 40 TiO2 30 SiO2 40 TiO2 30 SiO2 40 TiO2 30 SiO2 40 TiO2 30SiO2 40 TiO2 30 SiO2 40 TiO2 20 SiO2 30 TiO2 20 SiO2 30 TiO2 20 SiO2 30TiO2 20 SiO2 30 TiO2 20 SiO2 30 TiO2 20 SiO2 30 TiO2 20 SiO2 30 TiO2 30SiO2 S0 TiO2 20 SiO2 40 TiO2 30 SiO2 S0 TiO2 20 SiO2 40 TiO2 30 SiO2 S0TiO2 20 SiO2 40 TiO2 20 SiO2 40 TiO2 20 SiO2 40 TiO2 20 SiO2 40 TiO2 20SiO2 40 TiO2 20 SiO2 S0 TiO2 20 SiO2 40 TiO2 20 SiO2 50 TiO2 20 SiO2 50TiO2 20 SiO2 50 TiO2 20 SiO2 S0 TiO2 20 SiO2 S0 TiO2 20 SiO2 60 TiO2 20SiO2 60 TiO2 20 SiO2 60 TiO2 20 SiO2 70 TiO2 20 SiO2 70 TiO2 20 SiO2 70TiO2 20 SiO2 20 SiO2 1000 

In an alternative embodiment, multiple thin layers may be deposited on anon-planar substrate surface. There are various ways to reshape a flatsubstrate surface into other kinds of surface profiles. For example,known micro machining techniques can be used to create a curved surface.Gray scale masks can also be used to create a surface relief pattern ona photoresist film, and such a pattern can be transferred downward toanother material below the photoresist film. As is illustrated in FIG.17( a), a U-shaped groove 801 can be created in a substrate 802, and amultilayer film 804 made of alternating layers of two materials can bedeposited in the U groove. A planarization processing step can be usedto create the bottom half 805 of a two-dimensional GRIN lens (FIG. 17(b)). A gray scale mask can be used to make a convex surface profile 806on the existing half-GRIN structure 805 (FIG. 17( c)), and more layers807 can be deposited on top of the convex surface to make atwo-dimensional GRIN lens 808 (FIG. 17( d)) for light focusingapplications in which focusing light in both the horizontal and verticaldirections is desired. Gray scale mask techniques are used in microlensfabrication and are described in the above-referenced co-pending U.S.patent application Ser. No. 10/083,674.

It should be noted that structures other than alternating layers of twomaterials could be used. For instance, a third material (or more) couldbe added in some alternative embodiments. In another alternativeembodiment, small size grains or dots of one material are embedded inanother material with the grains or dots having different density and/orgrain size distributions in different parts of the material. Also, wiresof one material can be embedded into another material, with the wireshaving a desired distribution of density or size. In addition, acombination of embedded grains and wires could be used, and this couldbe further combined with thin layers. Thus, any mixture of small sizestructures may be used to create graded refractive index devicessuitable for various applications.

A variety of materials can also be used, including amorphous andpolycrystalline materials. For example, silica (SiO₂ n=1.45) and titania(TiO₂, n=2.35) are in common use for making thin film filters foroptical fiber communication applications. Due to their relatively largerefractive index difference (about 0.9), they can be used to createeffective graded refractive index devices for many light focusingapplications. A number of other materials may also be used, such astantalum pentoxide (Ta₂O₅), zirconium oxide (ZrO₂), niobium pentoxide(Nb₂O₅), hafnium oxide (HfO₂), zinc oxide (ZnO), germanium oxide (GeO₂),lead oxide (PbO), yttrium oxide (Y₂O₃), aluminum oxide (Al₂O₃), siliconcarbide (SiC), titanium carbide (TiC), titanium nitride (TiN), chromiumnitride (CrN), carbon nitride (CN), carbon boride (CB), aluminum nitride(AlN), zinc selenide (ZnSe), barium fluoride (BaF₂), magnesium fluoride(MgF₂), diamond like carbon (DLC), silicon (Si), germanium (Ge),polyimide, bisbenzocyclobutene (BCB) and cyclized transparent opticalpolymer (CYTOP). It should be noted that the refractive index of some ofthese materials is quite large (e.g., for silicon, n=3.4). The choice ofmaterials can be varied, depending on the particular application.

One advantageous choice of materials is silicon (Si) and silica (SiO₂).When Si is combined with SiO₂, the effective refractive index of theresulting medium can vary by as much as about 1.9. This large variation,combined with the high refractive index of silicon, may be useful insome applications because of the short focal length and small spot size(0.4 μm in one simulation) that can be achieved.

The superlens described herein can be used for any electromagnetic beamsize (not necessarily 10 μm beam size). For example, the electromagneticbeam size can be of the order of about 50 μm or 62.5 μm to cover thecase of standard multimode fibers. The superlens structure can beaccordingly changed to enable efficient light coupling between such amultimode fiber and a semiconductor waveguide device.

In the above embodiments, it has been assumed that a parallelelectromagnetic beam is incident from the left and is focused in anotheroptical medium to the right of the superlens. However, electromagneticbeam can propagate in either direction. An example of electromagneticbeam being incident from the right is the case of light coupling from asemiconductor laser to a single mode fiber. For this case, light shouldtravel in the reverse direction, i.e., from right to left.

In addition to the fact that the total distance of light propagation inthe superlens medium can be made much less than in previous devices (ofthe order of about 10 μm), there are also no waveguide-relatedsidewalls; as a result, light propagation loss is substantially reduced.

Further, total thickness of the superlens need not be less than or equalto one focal length (a quarter of the GRIN medium pitch). If thesuperlens has a thickness that is between one quarter and half the pitchof the GRIN medium, a parallel incident beam emerges in the verticaldirection from the output surface in a divergent or collimated manner.Similarly, if the superlens has a thickness between half and threequarter the pitch of the GRIN medium, a parallel incident beam emergesfrom the output surface in a convergent manner in the verticaldirection. Hence, the effect in vertical direction is similar to thecase when the superlens thickness is within a quarter of the pitch.However, the horizontal focusing is different since the thickness haschanged. This argument can be further extended to even larger values ofthe superlens thickness and the present invention covers all such cases.In general, for a superlens with pitch f, if the superlens has thicknessbetween [(2n−1)/4]f and of/2, where n is a natural number, then aparallel incident beam emerges in the vertical direction from the outputsurface in a divergent or collimated manner. If the superlens hasthickness between of/2 and [(2n+1)/4]f, where n is a natural number,then a parallel incident beam emerges in the vertical direction from theoutput surface in a convergent manner.

As discussed above, when the length of the superlens is about half ofthe GRIN pitch, the superlens will transform light from one focal pointto another focal point. In an exemplary embodiment shown in FIGS. 18(a)-(d), an input beam 1805 is introduced by an input waveguide 1810 atan output end location 1815 of the input waveguide and is coupled intoan output waveguide 1820 at an input end location 1825 of the outputwaveguide. In other embodiments, the input beam can also be introducedby a free-space beam at location 1815. Likewise, the output beam canalso go into free-space propagation at location 1825. Furthermore, boththe input and output beams can originate from free-space propagation atlocation 1815 and go into free-space propagation at location 1825. Thepresence of one or both waveguides, while preferred in some situations,does not typically alter the nature of beam transformation through thesuperlens. In some other situations, however, they could shape the beamwavefront and intensity profiles in combination with the superlens suchas in the case of a tapered waveguide inside the superlens.

The middle optical axis of the superlens is at a midheight location ofthe superlens' physical structure and is oriented in a directionperpendicular to the direction of the refractive index variation of thesuperlens' refractive index profile at the mid height location. In FIG.18( a) the input waveguide 1810 and output waveguide 1820 share the sameoptical axis so there is no vertical position change. In an exemplaryembodiment, the vertically graded refractive index profile of the lenshas a maximum refractive index value at the point where the optical axisof the input and output waveguides lie. In another exemplary embodiment,this point coincides with the middle optical axis of the superlens. In acase where the input waveguide 1810 and output waveguide 1820 may notshare the same optical axis, the super lens may focus the light beamfrom one focal point to another focal point while changing the verticallocation of the focus, as shown in FIG. 18( b). In an exemplaryembodiment, the vertically graded refractive index profile of the lenshas a maximum refractive index value at the vertical mid-point (i.e., atthe middle optical axis of the superlens). The optical axis of the inputwaveguide 1810 lies below this middle optical axis and the optical axisof the output waveguide 1820 lies above this middle optical axis. Theembodiments described are for the purpose of illustration and notlimitation.

Referring to FIG. 18( c), the length of the superlens may be aboutone-quarter of the GRIN pitch, and thus the superlens may transformparallel incident light into a focal point. The refractive index profileof the superlens may be asymmetric with respect to the middle opticalaxis of the superlens. For example, it may have a low refractive indexon the top (away from an underlying substrate) and a high refractiveindex on the bottom (near to an underlying substrate). The lightincident from a small input waveguide 1810 at the bottom may exit thesuperlens parallel to the incident light but with a vertical positionchange.

Referring to FIG. 18( d), the input waveguide may be aligned with thebottom (base) of the superlens positioned on a substrate 1801 and belowthe middle optical axis of the superlens. The superlens may have a GRINstructure and may be asymmetric with a high refractive index on top(away from an underlying substrate) and a low refractive index at thebase (near to an underlying substrate). The input surface of thesuperlens may be perpendicular to the middle optical axis of thesuperlens, and the output surface of the superlens may have an obliqueangle (e.g., <90 degrees) with the middle optical axis of the superlens.In this example, the wavefront passing through the output surface of thesuperlens moves nonparallel with the middle optical axis of thesuperlens.

In one embodiment, the refractive index profile may be half-parabolic,i.e., n(y)=A(B−y)² with the peak of the profile (y=0) at the substrateand with B as a constant chosen so that n(y=0)=A*B and n(H)=A*(B−H)²,where H is the height of the superlens, n(0) is the refractive index ofthe superlens at a bottom layer of the lens near the substrate surface,and n(H) is the refractive index of the superlens at the top layer ofthe lens, where y is a vertical direction substantially perpendicular tothe middle optical axis of the superlens. In FIG. 18( a), FIG. 18( b),FIG. 18( c), and FIG. 18( d), the output end 1815 of the input waveguide1810 can be away from, touching, or penetrating into the lens. Asillustrated by FIG. 18( e), the distance of the lens surface 1840 to theinput waveguide end 1815 is L_(Lw-IN). L_(Lw-IN) is zero if the inputwaveguide end touches the lens surface. L_(LW-IN) is positive if theinput waveguide end penetrates the lens surface. L_(LW-IN) is negativeif the input waveguide end is away from and does not touch the lenssurface.

Likewise, as illustrated in FIG. 18( e), the input end 1825 of theoutput waveguide 1820 can be away from, touching, or penetrating intothe lens. The distance of the lens output surface 1860 to the outputwaveguide end 1825 is L_(Lw-OUT). L_(Lw-OUT) is zero if the outputwaveguide end touches the lens surface. L_(Lw-OUT) is positive if theoutput waveguide end penetrates the lens surface. L_(Lw-OUT) is negativeif the output waveguide end is away from and does not touch the lenssurface.

In an exemplary embodiment, the input waveguide may be an opticalwaveguide with a step refractive index, and the waveguide material maybe semiconductor (e.g., a silicon-on-insulator waveguide) and the outputwaveguide may be a single mode optical fiber. In general, the input oroutput waveguide may be any optical waveguide, such as those withmultiple-layers of refractive-index variation, as long as the waveguideguides propagating optical beam energy. The highest refractive index ofthe center waveguiding region is called the refractive index of thewaveguide core n_(co). The refractive index away from the waveguidingregion, where the intensity of the guided beam is small compared to itspeak intensity and is monotonically decreasing, as is known to thoseskilled in the art as the evanescence wave region, is called therefractive index of the waveguide cladding n_(cl). The superlens mayhave a GRIN structure with a low index n_(a) on top and a high indexn_(b) at the bottom. The input waveguide 1901 may be aligned with thebottom of the superlens, as shown in FIG. 19. The input waveguide 1901may be a silicon-on-insulator waveguide with a silicon waveguide coresize of 0.3 μm in the vertical direction, and the refractive indexprofile of the superlens may be parabolic with n=3.6 at the bottom ton=1.5 at the top. The strong lensing effect in the superlens may resultin an output beam of greater than about 6 μm in diameter over less than20 μm of propagation through the superlens, and the wavefront may bebent, giving a flat wavefront at the output surface of the superlens.

In one embodiment illustrated in FIG. 19( a), the input waveguide end1805 or the output waveguide end 1825 has a constant height “t”vertically and constant width “w” horizontally (vertical is in adirection substantially perpendicular to the surface of the substrateand horizontal is in a direction substantially parallel to the surfaceof the substrate). In one preferred embodiment, the wavelength of lightis λ=1500 nm, the input waveguide is a silicon waveguide where thesilicon dioxide cladding and the silicon waveguide core penetrate intothe superlens. The refractive index of the input waveguide core n_(co)is 3.4, the refractive index of the cladding is n_(cl)=1.5. Letn_(wg)=(n_(co) ²−n_(cl) ²)^(0.5), where t is around λ/(2n_(wg)) such ast=300 nm, and w is slightly larger than the full-width half-maximum(FWHM) mode width of a single-mode optical fiber so that w is around 12micrometers. The output waveguide is an optical fiber with fiber endslightly away from the output surface of the superlens.

In another embodiment illustrated in FIG. 19( b), the input waveguideend 1805 or the output waveguide end 1825 has a variable vertical sizealong its length. For example, it may be tapered from a vertical heightof c-in or c-out to a smaller vertical height of d-in or d-out over alength L_(cd-in) to L_(cd-out) along the direction of the superlens.When the size of an end of the waveguide is small enough so the lightcan no longer be confined strongly inside the waveguide, the mode sizeof the light propagating in the waveguide becomes larger as the size ofthe waveguide drops. As a result, the guided optical mode size may beenlarged at the waveguide end. In one preferred embodiment, thewavelength of light is λ=1500 nm, the input waveguide is a siliconwaveguide with a thin layer of silicon dioxide cladding where thesilicon waveguide core and the silicon dioxide cladding penetrate intothe superlens. The thickness of the silicon dioxide cladding layer is100 nm, c-in is 300 nm, d-in is 5 nm, and L_(cd-in) is 20 micrometerswith the entire L_(cd-in) inside the superlens. The output waveguide isan optical fiber with a fiber end slightly away from the output surfaceof the superlens.

In yet another embodiment illustrated in FIG. 19( c), the inputwaveguide end 1805 or the output waveguide end 1825 has a variablehorizontal size along its length. For example, it may be tapered downfrom a horizontal size of a-in 1880 or a-out 1885 to a smallerhorizontal size b-in 1890 or b-out 1895 over a length L_(ab-in) toL_(ab-out) along the direction of the superlens. In one embodiment, thedown taper reduces the size of the guided optical mode at the smallwaveguide end 1890 or 1895 compared to the size of the guided opticalmode at the larger section of the waveguide 1880 or 1885. In onepreferred embodiment, the wavelength of light is λ=1500 nm, the inputwaveguide is a silicon waveguide with a thin layer of silicon dioxidecladding where the silicon waveguide core and the silicon dioxidecladding penetrate into the superlens. The thickness of the silicondioxide cladding layer is 100 nm, a-in is 12 micrometers, b-in is 8micrometers, and L_(ab-in) is 50 micrometers with a portion of L_(cd-in)outside the superlens. The output waveguide is an optical fiber having afiber end slightly away from the output surface of the superlens.

However, in another embodiment, when the size of an end of the waveguideis small enough (smaller than λ/2n_(wg), where n_(wg)=(n_(co) ²−n_(cl)²)^(0.5 with n) _(co) being the refractive index of the waveguide coreand n_(cl) being the refractive index of the cladding material aroundthe waveguide core) so that light can no longer be confined stronglyinside the waveguide, the down taper increases the size of the guidedoptical mode at the small waveguide end 1890 or 1895 compared to thesize of the guided optical mode at the larger section of the waveguide1880 or 1885. In one preferred embodiment, the wavelength of light isλ=1500 nm, the input waveguide is a silicon waveguide with a thin layerof silicon dioxide cladding where the silicon waveguide core and thesilicon dioxide cladding penetrate into the superlens. The thickness ofthe silicon dioxide cladding layer is 100 nm, a-in is 300 nm, b-in is 5nm, and L_(ab-in) is 10 micrometers with the entire L_(cd-in) inside thesuperlens. The output waveguide is an optical fiber having a fiber endslightly away from the output surface of the superlens.

Alternatively, in another embodiment shown in FIG. 19( d) the opticalwaveguide may be tapered vertically to a larger size at the waveguideend, and the size of the optical mode inside the waveguide may beenlarged at the waveguide end. The input waveguide may be verticallytapered up from c-in to d-in and/or the output waveguide may bevertically tapered up from c-out to d-out. In one preferred embodiment,the wavelength of light is λ=1500 nm, the input waveguide is a siliconwaveguide with a thin layer of silicon dioxide cladding where thesilicon waveguide core and the silicon dioxide cladding penetrate intothe superlens. The thickness of the silicon dioxide cladding layer is100 nm, c-in is 300 nm and d-in is 1 micrometer. The output waveguide isan optical fiber with fiber end slightly away from the output surface ofthe superlens.

Likewise, in another embodiment shown in FIG. 19( e), the opticalwaveguide may be tapered horizontally to a larger size at the waveguideend, and the size of the optical mode inside the waveguide may beenlarged at the waveguide end. The input waveguide may be horizontallytapered up from a-in to b-in and/or the output waveguide may behorizontally tapered up from a-out to b-out. In one preferredembodiment, the wavelength of light is λ=1500 nm, the input waveguide isa silicon waveguide with a thin layer of silicon dioxide cladding wherethe silicon waveguide core and the silicon dioxide cladding penetrateinto the superlens. The thickness of the silicon dioxide cladding layeris 100 nm, a-in is 300 nm and a-out is 12 micrometers. The outputwaveguide is an optical fiber with fiber end slightly away from theoutput surface of the superlens.

In another embodiment shown in FIG. 19( f), the end of the input and/oroutput waveguide may have a concave-curved surface towards the waveguideto change the curvature of the wavefront for the beam exiting and/orentering the waveguide. In yet another embodiment shown in FIG. 9( g),the end of the input and/or output waveguide may have a convex-curvedsurface. In yet another embodiment shown in FIG. 9( h), the end of theinput and/or output waveguide may have an arbitrary curvilinear surface.The curved surfaces mentioned above may be of curvilinear shapes ineither the vertical, or the horizontal, or both the vertical andhorizontal directions. Additionally, the end of the waveguide may taperup, taper down, or extend straight in either the vertical or horizontaldirection. In one preferred embodiment, the wavelength of light isλ=1500 nm, the input waveguide is a silicon waveguide with a thin layerof silicon dioxide cladding where the silicon waveguide core and thesilicon dioxide cladding penetrate into the superlens. The thickness ofthe silicon dioxide cladding layer is 100 nm, the input waveguide endhas a width of about 2 micrometers and has a concave horizontal shapetowards the waveguide with a radius of curvature of about 10micrometers. The output waveguide is an optical fiber with fiber endslightly away from the output surface of the superlens.

In yet another embodiment shown in FIG. 19( i), the input surface and/oroutput surface of the superlens may be a planar surface. In yet anotherembodiment shown in FIG. 19( j), the input surface and/or output surfaceof the superlens may be a curved surface to change the curvature of thewavefront for the beam exiting and/or entering the superlens, and thecurve may be of various concave (see FIG. 19( j)) or convex (see FIG.19( k)) or arbitrary curvilinear shapes (see FIG. 19( l)) in either thevertical, or the horizontal, or both the vertical and horizontaldirections. FIG. 19( j), FIG. 19( k), and FIG. 19( l) give illustrationsfor the cases in which the superlens output surface has curvature in thehorizontal direction.

In one preferred embodiment shown in FIG. 19( m), the wavelength oflight is λ=1500 nm, the input waveguide is a silicon waveguide with athin layer of silicon dioxide cladding where the silicon waveguide coreand the silicon dioxide cladding penetrate into the superlens. Thethickness of the silicon dioxide cladding layer is 100 nm, the inputwaveguide end has a width of about 2 micrometers and convex horizontallytowards the waveguide with a radius of curvature of about minus 10micrometers to generate a diverging wavefront from the incident planewavefront. The input surface of the superlens is a planar surface. Theoutput surface of the superlens is horizontally concave towards the lenshaving a radius of curvature of about 10 micrometers to recollimate thebeam by generating a planar wavefront. The output waveguide is anoptical fiber with fiber end slightly away from the output surface ofthe superlens.

In one embodiment in which the input waveguide end penetrates into thelens, the refractive index of the superlens material immediatelysurrounding the waveguide is of a lower value than the refractive indexof the waveguide. In another embodiment in which the input waveguide endpenetrates into the lens, at least part of the tapering is outside thesuperlens. In another embodiment in which the input waveguide endpenetrates into the lens, the entire tapering is outside the superlens.

In one embodiment in which the output waveguide end penetrates into thelens, the refractive index of the superlens material immediatelysurrounding the waveguide is of a lower value than the refractive indexof the waveguide. In another embodiment in which the output waveguideend penetrates into the lens, at least part of the tapering is outsidethe superlens. In another embodiment in which the output waveguide endpenetrates into the lens, the entire tapering is outside the superlens.

An exemplary superlens structure includes a large number (e.g., morethan 30 and up to a few hundred) of alternating thin layers of silica(SiO₂) and silicon (Si) on a flat silicon-on-insulator substrate. Thethickness of each layer (in nm) is provided in Table 3. The thicknessesof the silica layers range from 20 nm to 70 nm, and the thicknesses ofthe silicon layers range from 20 nm to 80 nm. In regions where theeffective index of refraction is high, silicon layers are near theirthickest while silica layers are near their thinnest; in regions wherethe effective index is low, the reverse applies.

TABLE 3 Mtl nm Si 60 SiO2 20 Si 50 SiO2 20 Si 60 SiO2 20 Si 50 SiO2 20Si 60 SiO2 20 Si 50 SiO2 20 Si 60 SiO2 20 Si 50 SiO2 20 Si 80 SiO2 30 Si80 SiO2 30 Si 80 SiO2 30 Si 80 SiO2 30 Si 80 SiO2 30 Si 80 SiO2 30 Si 80SiO2 30 Si 80 SiO2 30 Si 50 SiO2 20 Si 80 SiO2 30 Si 50 SiO2 20 Si 50SiO2 20 Si 50 SiO2 20 Si 50 SiO2 20 Si 50 SiO2 20 Si 50 SiO2 20 Si 50SiO2 20 Si 50 SiO2 20 Si 50 SiO2 20 Si 70 SiO2 30 Si S0 SiO2 20 Si 70SiO2 30 Si 70 SiO2 30 Si 70 SiO2 30 Si 50 SiO2 20 Si 40 SiO2 20 Si S0SiO2 20 Si 40 SiO2 20 Si 70 SiO2 30 Si 40 SiO2 20 Si 70 SiO2 30 Si 40SiO2 20 Si 70 SiO2 30 Si 40 SiO2 20 Si 40 SiO2 20 Si 40 SiO2 20 Si 40SiO2 20 Si 40 SiO2 20 Si 40 SiO2 20 Si 40 SiO2 20 Si 40 SiO2 20 Si 40SiO2 20 Si 40 SiO2 20 Si 40 SiO2 20 Si S0 SiO2 30 Si 40 SiO2 20 Si 50SiO2 30 Si 40 SiO2 20 Si S0 SiO2 30 Si 40 SiO2 20 Si 30 SiO2 20 Si 40SiO2 20 Si 30 SiO2 20 Si 40 SiO2 20 Si 40 SiO2 30 Si 40 SiO2 20 Si 40SiO2 30 Si 40 SiO2 20 Si 40 SiO2 30 Si 30 SiO2 20 Si 30 SiO2 20 Si 30SiO2 20 Si 30 SiO2 20 Si 30 SiO2 20 Si 30 SiO2 20 Si 30 SiO2 20 Si 30SiO2 20 Si 30 SiO2 20 Si 40 SiO2 30 Si 40 SiO2 30 Si 40 SiO2 30 Si 40SiO2 30 Si 40 SiO2 30 Si 40 SiO2 30 Si 40 SiO2 30 Si 20 SiO2 20 Si 40SiO2 30 Si 20 SiO2 20 Si 40 SiO2 30 Si 20 SiO2 20 Si 40 SiO2 30 Si 20SiO2 20 Si 20 SiO2 20 Si 40 SiO2 30 Si 20 SiO2 20 Si 20 SiO2 20 Si 20SiO2 20 Si 20 SiO2 20 Si 20 SiO2 20 Si 20 SiO2 20 Si 20 SiO2 20 Si 20SiO2 20 Si 20 SiO2 20 Si 20 SiO2 20 Si 20 SiO2 20 Si 20 SiO2 20 Si 20SiO2 20 Si 20 SiO2 20 Si 20 SiO2 20 Si 20 SiO2 20 Si 20 SiO2 40 Si 30SiO2 20 Si 20 SiO2 20 Si 20 SiO2 40 Si 30 SiO2 20 Si 20 SiO2 20 Si 20SiO2 40 Si 30 SiO2 20 Si 30 SiO2 40 Si 30 SiO2 40 Si 30 SiO2 40 Si 30SiO2 40 Si 30 SiO2 40 Si 30 SiO2 40 Si 20 SiO2 30 Si 20 SiO2 30 Si 20SiO2 30 Si 20 SiO2 30 Si 20 SiO2 30 Si 20 SiO2 30 Si 20 SiO2 30 Si 30SiO2 S0 Si 20 SiO2 40 Si 30 SiO2 S0 Si 20 SiO2 40 Si 30 SiO2 S0 Si 20SiO2 40 Si 20 SiO2 40 Si 20 SiO2 40 Si 20 SiO2 40 Si 20 SiO2 40 Si 20SiO2 S0 Si 20 SiO2 40 Si 20 SiO2 50 Si 20 SiO2 50 Si 20 SiO2 50 Si 20SiO2 S0 Si 20 SiO2 S0 Si 20 SiO2 60 Si 20 SiO2 60 Si 20 SiO2 60 Si 20SiO2 70 Si 20 SiO2 70 Si 20 SiO2 70 Si 20 SiO2 20

The fabrication methods for the superlens structure described aboveexist in the prior art. The GRIN film can be deposited using a varietyof well-established technologies; for example, existing technologies forfabricating thin film dense wavelength division multiplexing (DWDM)filters for optical communications by depositing successive layers ofmaterials can be adapted to fabricating GRIN devices. Deposition methodsthat may be employed to create the structure include sputtering,chemical vapor deposition, electron beam and thermal evaporation, ionbeam deposition or dual ion beam deposition (also called ion assisteddeposition, or IAD), sol gel spin or dip coating and others.

The curved input and output sidewall surface formations are achievedthrough photolithography and etching. This method is illustrated using aflowchart in FIG. 20. The fabrication step begins with the deposition ofGRIN film as shown in step 1102. In step 1104, a metal layer or apolysilicon layer, which is later used as dry etch mask, is deposited ontop of the GRIN film. A photoresist film is then spin-coated on themetal or polysilicon film in step 1106. The horizontal curved surfacepattern is then made on a standard photomask in step 1108. The patternis then transferred to the photoresist layer using UV exposure with thehelp of a standard mask aligner in step 1110. After the development ofthe photoresist, dry etching is employed to transfer the horizontalpattern from the photoresist to the metal or polysilicon in step 1112.Finally, in step 1114, dry etching of the GRIN film creates the desiredcurved surface structure by using the metal or polysilicon pattern as adry etch mask. The curved sidewall profile is controlled by varying theplasma processing parameters such as temperature, induction coupledplasma power or RF power, DC biased voltage, chamber pressure and gasmixture.

An example of the dry etched vertical input sidewall of a superlens isshown in FIG. 21. While FIG. 21 shows a scanning electron microscopeimage of a vertical straight input sidewall, it is also possible tocreate vertically curved sidewall. This can be done by changing theplasma processing parameters, or by combining dry etching with wetetching. FIG. 22 shows such a case. The present invention also allowsthe use of dry or wet etching process to create desirable sidewallsurface profiles of the superlens according to the needs.

The superlens structure of the present invention can be fabricated onany solid substrate. For example, the superlens can be directlyfabricated on a Si, or GaAs, or InP substrate together with photonic andelectronic ICs as well as fiber positioning grooves such as V orU-groove. In such a case, the connection between a superlens and channelwaveguide is defined using photolithography, which provides inherenthigh precision alignment. Further, such a structure can be used in thesame way as a lensed fiber. The superlens can also be fabricated on asubstrate next to a flip-chip bonding area. This ensures that when aphotonic chip is flip-bonded next to the superlens, its output beam iscircularized. As a combination of the above two case, a superlens can befabricated in between a fiber positioning V-groove and a flip-chipbonding region. The combined structure enables one to achieve completelypassive fully automated photonic chip packaging and fiber pig-tailing.

Further, the superlens can also be fabricated in an array form. Thearray form superlens can then be applied to multichannels light couplinginto or out of a multi-port photonic chip. This is very difficult toachieve using individual lensed fibers. An example of array formsuperlens coupled to multi-port photonic chip is shown in FIG. 23.

As a further extension, the substrate material can be Si withmicroelectronic circuits for driving the photonic chip as well as forsignal processing. The superlens can be fabricated on the Si substratenext to the photonic flip-chip bonding region. An advantage of such anarrangement is that the short distance between the photonic chip and theelectronics circuits improves high-speed communication between opticsand electronics.

While the preferred embodiment of the present invention is applicable toelectromagnetic beam focusing, it can also be used in otherapplications. One example is in near-field optics for the transformationof an electromagnetic beam to a small mode size. In the existingtechnology, the transformation is achieved by tapering the fiber to asmall tip (e.g., tens of nanometers) at one end and coating the outsideof the tapered region with a metal film to prevent light from escaping.However, by this method, most of the light (as much as 99.99%) is lostduring the electromagnetic beam size transformation process. Replacingsuch tapered fibers with the superlens of the present invention canimprove the transmission efficiency substantially.

Another application relates to optical data storage, where the storagedensity can be limited by the spot size of light beams used to recordand/or read the data. In existing optical storage devices, discreteoptical elements (prisms, lenses, wave plates, etc.) are used to makethe optical head and to focus a light beam from a semiconductor laser toa spot size of a few microns. Using a GRIN device, the focused spot sizemay be made much smaller, and the storage density may be substantiallyincreased. In addition, discrete optical elements can also be replacedwith planar light wave circuit based integrated optics.

GRIN devices may be used in any application where there is a need tofocus a light beam into a small spot size. For example, such couplerscan be used to focus light from a single mode optical fiber into a III-Vsemiconductor waveguide, in place of objective lenses or lens tippedfibers. Through proper selection of the refractive index distribution,mode matching to the fiber and the semiconductor waveguide can beachieved. Such devices can be fabricated on a substrate as part of anintegrated coupler structure that includes a U-groove or V-groove forholding an optical fiber and a photonic chip mounting recess for holdingthe semiconductor waveguide.

In addition to light beam focusing, GRIN devices can also be used inother applications. For instance, in many near field opticsapplications, transformation of a light beam from a mode profilecorresponding to a standard single mode optical fiber to a smaller modesize is generally achieved by tapering the fiber to a small tip (e.g.,tens of nanometers) at one end and coating the outside of the taperedregion with a metal film to prevent light from escaping. In general,most of the light (as much as 99.99%) is lost during this beam sizetransformation process. Replacing such tapered fibers with GRIN devicescan improve the transmission efficiency substantially.

Although the present invention has been described in considerable detailwith reference to certain embodiments thereof, other embodiments arepossible without departing from the present invention. The spirit andscope of the appended claims should not be limited, therefore, to thedescription of the preferred embodiments included here. All embodimentsthat come within the meaning of the claims, either literally or byequivalence, are intended to be embraced therein. Furthermore, theadvantages described above are not necessarily the only advantages ofthe invention, and it is not necessarily expected that all of thedescribed advantages will be achieved with every embodiment of theinvention.

The invention claimed is:
 1. An apparatus for coupling light betweeninput and output waveguides, the apparatus comprising: a substrate; aninput waveguide disposed on the substrate and comprising a first opticalaxis; an output waveguide disposed on the substrate and comprising asecond optical axis vertically offset from the first optical axis; asuperlens disposed on the substrate between the input waveguide and theoutput waveguide, the superlens having a middle optical axis andcomprising a vertically graded refractive index film having a refractiveindex distribution n(y), where y is a vertical direction substantiallyperpendicular to the middle optical axis.
 2. The apparatus of claim 1,wherein the refractive index distribution n(y) is symmetric about themiddle optical axis.
 3. The apparatus of claim 2, wherein the refractiveindex distribution n(y) is parabolic.
 4. The apparatus of claim 1,wherein the refractive index distribution n(y) is asymmetric about themiddle optical axis.
 5. The apparatus of claim 4, wherein the refractiveindex distribution is half-parabolic.
 6. The apparatus of claim 4,wherein the refractive index distribution increases in the verticaldirection away from the substrate.
 7. The apparatus of claim 4, whereinthe refractive index distribution decreases in the vertical directionaway from the substrate.
 8. The apparatus of claim 1, wherein thesubstrate is a semiconductor substrate.
 9. The apparatus of claim 1,wherein the input waveguide comprises a smaller vertical size than thesuperlens, and the output waveguide comprises a larger vertical sizethan the superlens, the second optical axis being vertically offset fromthe first optical axis in a direction away from the substrate.
 10. Theapparatus of claim 9, wherein the vertical size of the input waveguideis about 0.5 micron or less, and the vertical size of the outputwaveguide is about 5 microns or more.
 11. The apparatus of claim 1,wherein a length of the superlens between the input and outputwaveguides is about 20 microns or less.
 12. The apparatus of claim 1,wherein the input waveguide comprises a silicon-on-insulator waveguidewith a silicon waveguiding core.
 13. The apparatus of claim 1, whereinthe output waveguide comprises an optical fiber.
 14. The apparatus ofclaim 13, wherein the semiconductor substrate includes a fiberpositioning groove for the optical fiber.
 15. The apparatus of claim 1,wherein the vertically graded refractive index film comprises aplurality of layers of at least two alternating materials.
 16. Theapparatus of claim 15, wherein the at least two alternating materialsinclude Si and SiO₂.
 17. The apparatus of claim 16, wherein the layersof Si comprise a thickness ranging from about 20 nm to about 80 nm. 18.The apparatus of claim 16, wherein the layers of SiO.sub.2 comprise athickness ranging from about 20 nm to about 70 nm.
 19. The apparatus ofclaim 15, wherein the plurality of layers comprises at least 30 layers.20. The apparatus of claim 1, wherein an input surface of the superlensadjacent to the input waveguide is substantially perpendicular to themiddle optical axis, and wherein an output surface of the superlensadjacent to the output waveguide comprises an oblique angle with respectto the middle optical axis.
 21. The apparatus of claim 1, wherein atleast a portion of the input waveguide has a variable vertical sizealong a length of the input waveguide, the portion being a verticallytapered portion.
 22. The apparatus of claim 21, wherein the verticallytapered portion of the input waveguide tapers from a larger verticalsize to a smaller vertical size in a direction toward the superlens. 23.The apparatus of claim 21, wherein the vertically tapered portion of theinput waveguide tapers from a smaller vertical size to a larger verticalsize in a direction toward the superlens.
 24. The apparatus of claim 1,wherein at least a portion of the input waveguide has a variablehorizontal size along a length of the input waveguide, the portion beinga horizontally tapered portion.
 25. The apparatus of claim 24, whereinthe horizontally tapered portion of the input waveguide tapers from alarger horizontal size to a smaller horizontal size in a directiontoward the superlens.
 26. The apparatus of claim 24, wherein thehorizontally tapered portion of the input waveguide tapers from asmaller horizontal size to a larger horizontal size in a directiontoward the superlens.
 27. The apparatus of claim 1, wherein at leastpart of the input waveguide is inside the superlens.
 28. The apparatusof claim 27, wherein the part of the input waveguide inside thesuperlens is a tapered portion of the input waveguide.
 29. The apparatusof claim 1, wherein the input waveguide is entirely outside thesuperlens.
 30. The apparatus of claim 1, wherein at least a portion ofthe output waveguide has a variable vertical size along a length of theoutput waveguide, the portion being a vertically tapered portion. 31.The apparatus of claim 30, wherein the vertically tapered portion of theoutput waveguide tapers from a larger vertical size to a smallervertical size in a direction toward the superlens.
 32. The apparatus ofclaim 30, wherein the vertically tapered portion of the output waveguidetapers from a smaller vertical size to a larger vertical size in adirection toward the superlens.
 33. The apparatus of claim 1, wherein atleast a portion of the output waveguide has a variable horizontal sizealong a length of the output waveguide, the portion being a horizontallytapered portion.
 34. The apparatus of claim 33, wherein the horizontallytapered portion of the output waveguide tapers from a larger horizontalsize to a smaller horizontal size in a direction toward the superlens.35. The apparatus of claim 33, wherein the horizontally tapered portionof the output waveguide tapers from a smaller horizontal size to alarger horizontal size in a direction toward the superlens.
 36. Theapparatus of claim 1, wherein at least part of the output waveguide isinside the superlens.
 37. The apparatus of claim 36, wherein the part ofthe output waveguide inside the superlens is a tapered portion of theoutput waveguide.
 38. The apparatus of claim 1, wherein the outputwaveguide is entirely outside the superlens.
 39. The apparatus of claim1, wherein at least one of the input waveguide and the output waveguidecomprise a curvilinear end surface.
 40. The apparatus of claim 39,wherein the curvilinear end surface is convex toward the superlens. 41.The apparatus of claim 39, wherein the curvilinear end surface isconcave toward the superlens.
 42. The apparatus of claim 39, wherein thecurvilinear end surface has an arbitrary curvilinear shape.
 43. Theapparatus of claim 1, wherein the superlens comprises an input surfaceand an output surface, and at least one of the input surface and theoutput surface comprises a curvilinear shape.
 44. The apparatus of claim43, wherein the input surface is concave towards the input waveguide.45. The apparatus of claim 43, wherein the input surface is convextowards the input waveguide.
 46. The apparatus of claim 43, wherein thecurvilinear shape is an arbitrary curvilinear shape.
 47. The apparatusof claim 43, wherein the output surface is concave towards the outputwaveguide.
 48. The apparatus of claim 43, wherein the output surface isconvex towards the output waveguide.
 49. The apparatus of claim 1,wherein the superlens comprises an input surface and an output surface,and at least one of the input surface and the output surface is a planarsurface.
 50. An optical apparatus comprising: a substrate; an inputwaveguide and/or an output waveguide disposed on the substrate; and asuperlens disposed on the substrate adjacent to the input waveguideand/or the output waveguide, the superlens having a lens optical axisand comprising a vertically graded refractive index film having arefractive index distribution n(y), where y is a vertical directionsubstantially perpendicular to the lens optical axis, and where theinput and/or output waveguide disposed on the substrate comprises anoptical axis disposed substantially parallel to a plane of thesubstrate.
 51. The optical apparatus of claim 50, wherein the verticallygraded refractive index film comprises a plurality of alternating layersof a first material and a second material, each layer of the secondmaterial having a thickness substantially less than an effectivewavelength of light in the second material, wherein at least one of thefirst and second materials is an amorphous material, the first materialhaving a first index of refraction, the second material having a secondindex of refraction different from the first index of refraction, theplurality of alternating layers forming a light transmitting medium withan effective index of refraction in a local region that depends on alocal ratio of a volume of the layers of the first material to a volumeof the layers of the second material, wherein a graded effective indexof refraction along a direction transverse to the layers is formed byvarying the thicknesses of the layers.
 52. The apparatus of claim 1,wherein the vertically graded refractive index film comprises aplurality of alternating layers of a first material and a secondmaterial, each layer of the second material having a thicknesssubstantially less than an effective wavelength of light in the secondmaterial, wherein at least one of the first and second materials is anamorphous material, the first material having a first index ofrefraction, the second material having a second index of refractiondifferent from the first index of refraction, the plurality ofalternating layers forming a light transmitting medium with an effectiveindex of refraction in a local region that depends on a local ratio of avolume of the layers of the first material to a volume of the layers ofthe second material, wherein a graded effective index of refractionalong a direction transverse to the layers is formed by varying thethicknesses of the layers.